I actually don't think any new who story would work with classic era Doctors.
I remember Bob Holmes and Terrance Dicks both said that the single most important thing was not to change the character of the Doctor too much.
Basically they always wrote the Doctor as being the same character. They'd maybe make a few allowances, like obviously an actor like Troughton wouldn't be given as many fight scenes, but basically the Doctor was always the Doctor to them, and they'd let the actor reinterpret the lines differently.
Pertwee would be deadly serious in his delivery, Tom would be flippant and humorous, (and might change the odd line somewhere to better suit him), but the Doctors core character would be the same.
That's how you always should write the Doctor. Remember that its his outer personality that changes. His core persona, his consciousness and his memories are the same from incarnation to incarnation. So really from the writers perspective he is kind of the same, and its the actors job to try and make it different whilst staying within the template the writers set down.
In New Who however the problem is that the writers evidently HATED the template for the Classic era Doctors, hence why they changed it in every way. They removed big things like his reasons for travelling, his more level headed, practical nature, his moral code, his asexuality, even little things like his dress sense and fighting skills.
With this in mind how would Pertwee fit into the Tennant two parter? Can you imagine Pertwee giving people shit about using guns? Telling Martha off for joining the military? How would any of the first 7 fit into the Matt Smith Angels two parter? Can you imagine them crying when someone got killed? Having to fend off their companion trying to come on to them?
Can you imagine ANY of the first 7 doing the bit in Dalek with Eccelston going ROSE I WASN'T, I COULDN'T.
It would be fucking hysterical meanwhile trying to crowbar Pertwee or Tom into Doomsday?
I actually don't think a lot of old who Doctors would be in New Who stories. Tom Baker used to fight with guys like Graham Williams and Bob Holmes over their scrips because he thought their stories weren't up to scratch.
He was a total dick to Louise Jameson because thought Leela of all companions was rubbish. Leela that unbelievable badass, played by one of the best actresses in DW, who went on to have leading roles in other international series, and who inspired another iconic, kickass character in name and personality in another sci fi classic.
If she's not good enough, what would Tom have made of fucking Clara! Or Mandip for that matter LOL. I shudder to think of the tantrum we'd have seen if old Tom had been handed Rosa or Hellbent.